Question

Two dice are thrown at the same time. Find the probability that the sum of two numbers appearing on the top of the dice is more than 9.

Answer 1

When two dice are thrown simultaneously, the possible outcomes are :
(1,1); (1,2); (1,3); (1,4); (1,5); (1,6)
(2,1); (2,2); (2,3); (2,4); (2,5); (2,6)
(3,1); (3,2); (3,3); (3,4); (3,5); (3,6)
(4,1); (4,2); (4,3); (4,4); (4,5); (4,6)
(5,1); (5,2); (5,3); (5,4); (5,5); (5,6)
(6,1); (6,2); (6,3); (6,4); (6,5); (6,6)
Number of possible outcomes = 36
Let E be the event that the sum of the numbers appearing on the top of the two dice is more than 9.
The favourable outcomes are:
(4, 6), (5, 5), (5, 6), (6, 4), (6, 5) ,(6, 6)
Number of favourable outcomes = 6
∴ P(getting a sum more than 9) = P(E) = $\frac{6}{36}=\frac{1}{6}$